garch vs garchFit - minimum sample size
Dear Yohan:
Thanks for your work on this.
If you haven't already, could you please add descriptions of the
arguments delta, skew and shape to the help page: How are they defined,
e.g., relative to what distribution -- and which parameterization of
that distribution? For example, are these passed to documented R
function(s)? Also or alternatively, can you site a relevant Wikipedia
article?
In particular, can Student's t be obtained as a special case? I
need this for my work with the FinTS package.
Thanks again,
Spencer Graves
Yohan Chalabi wrote:
"AZ" == Achim Zeileis <Achim.Zeileis at wu-wien.ac.at>
on Wed, 13 Feb 2008 22:22:58 +0100 (CET)
AZ> As far as I can see, Diethelm and Yohan have been quite busy AZ> improving AZ> the optimizers and also their documentation (which seems to AZ> be more AZ> detailed in the devel-version of the package, maybe Yohan AZ> or Diethelm AZ> can comment on this). I think (but might be wrong here) that all AZ> optimizers used by garchFit() rely on numerical gradients AZ> and numerical AZ> Hessians. We have implemented a new optimization scheme "mnfb" in the devel-version of fGarch (https://svn.r-project.org/Rmetrics/trunk/fGarch). It is actually the same fortran library as used in the R function nlminb(). But we have implemented the whole optimization in fortran. As you have noticed it, we are also working on the documentation and we hope the new manual page is more readable. AZ> Adrian's code comes with its own optimzer (Quasi-Newton) which AZ> is not AZ> available in garchFit() (I think) and provides both analytical AZ> and AZ> numerical gradients (Gaussian conditional distribution only). In garchFit you can choose between 5 different optimizations schemes : "nlminb" , "mnfb" (in devel-version), "sqp", "lbfgsb", "nlminb+nm", "lbfgsb+nm". Please read the man page for more details. Although the analytical gradient and hessian of ARMA-APARCH for Gaussian conditional distribution can be calculated without too much of effort, the analytical solutions for other distribution are not trivial. Since garchFit can handle different conditional distributions ("norm", "snorm", "ged", "sged", "std", "sstd"), we decieded to use only numerical approximations. regards, Yohan